   Test Coils Data

The resistance of each coil was determined by passing a known current through the coil and measuring the voltage drop across the terminals of the coil. Three different current settings were used and the average resistance determined. As a comparison the resistance was also calculated from the coil parameters using the coil resistance equation as derived in the theory section. The inductance of each coil was also determined by direct measurement using a multimeter (method 1) and also by the inductance measuring method described in the theory section (method 2). The number of turns in each coil is a calculated quantity with the exception of the sensor coils which were counted (I was too lazy to count the turns as I wound the coils). Coils C and D show a notable difference between the inductance values obtained using the two methods, it's not entirely clear why this is the case but it can be accounted for in part by the inherent error of the multimeter measurements at low values. The inductance values are also determined by calculation using the inductance formula which can be found in the theory section. There is a significant difference between the measured and calculated values for the drive coils. As mentioned earlier, N is an estimated value based on the dimensions of the windings and since the result depends on N2 this is the most likely source of the discrepancy. The calculated result is in much better agreement when the number of turns is accurately known, as in the case of the sensor coil.

The treatment of errors is not 100% rigorous, I've put them in to remind myself they exist! The firm adherence to significant figures is also a bit ropey. I'll tighten this up later.

Something which is worth noting is that the coil time constants vary much less than the inductance values which range over more than an order of magnitude.

The coil data are tabulated below:

 Coil A Voltage (V) 2.6 +/- 0.05 5.3 +/- 0.05 8.5 +/-0.05 Current (A) 2.0 +/- 0.05 4.0 +/- 0.05 6.0 +/- 0.05 Resistance ( ) 1.30 +/- 0.04 1.325 +/- 0.025 1.417 +/- 0.020 Average Resistance ( ) 1.35 +/- 0.03 Calculated Resistance ( ) 1.40 Number of Turns 480 Outer Radius (mm) 19.4 Inner Radius (mm) 7 Length (mm) 25.7 Wire Diameter (mm) 0.8 Inductance (mH) method 1 2.04 Inductance (mH) method 2 1.98 Calculated Inductance (mH) 2.91 Time Constant (ms) 1.49

 Coil B Voltage (V) 1.1 +/- 0.05 2.2 +/- 0.05 3.3 +/- 0.05 Current (A) 2.0 +/- 0.05 4.0 +/- 0.05 6.0 +/- 0.05 Resistance ( ) 0.55 +/- 0.04 0.55 +/- 0.02 0.550 +/- 0.013 Average Resistance ( ) 0.55 +/- 0.02 Calculated Resistance ( ) 0.52 Number of Turns 300 Outer Radius (mm) 18.5 Inner Radius (mm) 7 Length (mm) 26.3 Wire Diameter (mm) 1.0 Inductance (mH) method 1 0.798 Inductance (mH) method 2 0.763 Calculated Inductance (mH) 1.08 Time Constant (ms) 1.39

 Coil C Voltage (V) 0.49 +/- 0.005 0.97 +/- 0.005 1.4 +/- 0.05 Current (A) 2.0 +/- 0.05 4.0 +/- 0.05 6.0 +/- 0.05 Resistance ( ) 0.245 +/- 0.009 0.243 +/- 0.004 0.233 +/- 0.011 Average Resistance ( ) 0.24 +/- 0.01 Calculated Resistance ( ) 0.23 Number of Turns 180 Outer Radius (mm) 18.9 Inner Radius (mm) 7 Length (mm) 26.7 Wire Diameter (mm) 1.25 Inductance (mH) method 1 0.316 Inductance (mH) method 2 0.253 Calculated Inductance (mH) 0.392 Time Constant (ms) 1.05

 Coil D Voltage (V) 0.28 +/- 0.005 0.56 +/- 0.005 0.82 +/- 0.005 Current (A) 2.0 +/- 0.05 4.0 +/- 0.05 6.0 +/- 0.05 Resistance ( ) 0.140 +/- 0.006 0.140 +/- 0.003 0.137 +/- 0.002 Average Resistance ( ) 0.14 +/- 0.04 Calculated Resistance ( ) 0.11 Number of Turns 130 Outer Radius (mm) 18.3 Inner Radius (mm) 7 Length (mm) 27.5 Wire Diameter (mm) 1.5 Inductance (mH) method 1 0.167 Inductance (mH) method 2 0.099 Calculated Inductance (mH) 0.195 Time Constant (ms) 0.707

 Sensor Coil Resistance ( ) 48.4 +/- 0.05 Calculated Resistance ( ) 44.5 Number of Turns 500 Outer Radius (mm) 24.5 Inner Radius (mm) 22 Length (mm) 9 Wire Diameter (mm) 0.2 Inductance (mH) method 1 18.08 Inductance (mH) method 2 Calculated Inductance (mH) 17.34

 2 Stage Coilgun - Drive Coil 1 Voltage (V) 0.84 +/- 0.005 1.72 +/- 0.005 2.60 +/- 0.005 Current (A) 2.0 +/- 0.05 4.0 +/- 0.05 6.0 +/- 0.05 Resistance ( ) 0.42 0.43 0.43 Average Resistance ( ) 0.43 Calculated Resistance ( ) 0.41 Number of Turns 240 Outer Radius (mm) 17.2 Inner Radius (mm) 7.5 Length (mm) 25.4 Wire Diameter (mm) 1.0 Inductance (mH) method 1 0.522 Inductance (mH) method 2 0.444 Calculated Inductance (mH) 0.692 Time Constant (ms) 0.97

 2 Stage Coilgun - Sensor Coil 1 Resistance ( ) 11.1 +/- 0.05 Calculated Resistance ( ) 12.8 Number of Turns 150 Outer Radius (mm) 18.5 Inner Radius (mm) 17.2 Length (mm) 6.5 Wire Diameter (mm) 0.2 Inductance (mH) method 1 1.01 Inductance (mH) method 2

 2 Stage Coilgun - Drive Coil 2 Voltage (V) 0.83 +/- 0.005 1.65 +/- 0.005 2.49 +/- 0.005 Current (A) 2.0 +/- 0.05 4.0 +/- 0.05 6.0 +/- 0.05 Resistance ( ) 0.42 0.41 0.42 Average Resistance ( ) 0.42 Calculated Resistance ( ) 0.41 Number of Turns 240 Outer Radius (mm) 17.0 Inner Radius (mm) 7.5 Length (mm) 26.1 Wire Diameter (mm) 1.0 Inductance (mH) method 1 0.538 Inductance (mH) method 2 0.453 Calculated Inductance (mH) 0.675 Time Constant (ms) 1.02

 2 Stage Coilgun - Sensor Coil 2 Resistance ( ) 11.0 +/- 0.05 Calculated Resistance ( ) 14.0 Number of Turns 150 Outer Radius (mm) 18.5 Inner Radius (mm) 17.0 Length (mm) 6.2 Wire Diameter (mm) 0.2 Inductance (mH) method 1 1.05 Inductance (mH) method 2  